Definition 2 ([1]}) 
A matching in the context of SRI is a partition of a subset of agents into disjoint pairs. If agent \(a_i\)  is in one of the pairs in the matching, we say that \(a_i\)  is matched. Otherwise, we say \(a_i\)  is unmatched. Moreover, if agent \(a_i\)  is in a pair with agent \(a_j\) , we say that \(a_j\)  is \(a_i\) 's partner.

